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Updated in [August 13th, 2023]

Skills and Knowledge Acquired:
This course will provide students with the skills and knowledge necessary to become a full master of Calculus 1. Students will learn the basics of Calculus 1 through animation, graphical and mathematical proofs, and hundreds of numerical practice problems with complete solutions. The lectures are designed to be appealing, fancy, fast, and efficient, making them a perfect choice for high school and college students. Through this course, students will acquire knowledge of functions, domains and ranges, inverse functions, vertical and horizontal line tests, ordered pair tests, graphing of functions, transformations of functions, parabolas, inverse parabolic functions, circles, centers and radii of circles, radians and degrees of circles, least squares methods, least square lines/regression lines, limits, continuity and discontinuity, asymptotes, holes, point-slope form of equations, slope-intercept form of equations, standard form of equations, tangent and normal lines, derivatives, chain rule, power rule, product rule, quotient rule, derivatives of trigonometric functions, inverse trigonometric functions, hyperbolic functions, inverse hyperbolic functions, composite functions, implicit differentiation, logarithmic and exponential rules, logarithmic and exponential differentiation, squeeze theorem, and modeling and solving equations.


Contribution to Professional Growth:
This course contributes to professional growth by providing a comprehensive overview of Calculus 1. It covers a wide range of topics, including functions, domain and range, inverse functions, graphing, transformations, parabolas, circles, least squares methods, limits, continuity and discontinuity, asymptotes, tangent and normal lines, derivatives, chain rule, power rule, product rule, quotient rule, trigonometric functions, inverse trigonometric functions, hyperbolic functions, inverse hyperbolic functions, composite functions, implicit differentiation, logarithmic and exponential rules, logarithmic and exponential differentiation, squeeze theorem, and modeling and solving equations. The course also includes videos, explanations, graphical and mathematical proofs, hundreds of numerical practice problems with complete solutions, and appealing, fancy graphic designs. This comprehensive overview of Calculus 1 provides students with the knowledge and skills necessary to succeed in high school and college, and can help them to develop the skills needed for professional growth.


Suitability for Further Education:
This course is suitable for preparing further education as it covers a wide range of topics related to calculus 1. It includes videos explanation with basics, graphical and mathematical proofs, hundreds of numerical practice problems with complete solutions, and animation to help students understand the content. The course also covers 42.5 hours of content, 59 sections, 370+ lectures, 327 areas, 325 figures and tables, and 556 solved numerical problems with complete solutions. Additionally, the lectures are appealing, fancy, fast, and take less time to walk students through the content. This makes it a perfect choice for students who take high school and college.

Course Syllabus

Introduction

Function

Domain and Range of a Function - Domain and Range from graphs

Domain and Range of a Function - Polynomial, Fractional and Root functions

Ordered pair tests, One-to-One and Onto Functions

Vertical line Tests, Horizontal line Tests

Graphing of Functions

Transformation of graph of a Function

Function - Composite Functions

Inverse Functions - Introduction to Inverse Function

Inverse Functions - Find Inverse Functions from graphs

Inverse Functions - Identify the Inverse Functions from equation

Parabola - Introduction to Parabola

Parabola - Problem solutions using Method 1, 2 & 3 and also integer/odd method

Point slope, Slope intercept and Standard form of the equation

Tangent and Normal lines

Circle - Center, Radius and Equation of a Circle

Circle - Center and Radius from the graph of a circle

Circle - Center and Radius of a circle from completing the square

Circle - Radians & Degrees of a circle

Curve fitting - Least Square lines / Regression lines

Curve fitting - Group averages method

Limit - Introduction

Limit - Procedures to find the limit

Limit - Limit of Trigonometric functions

Limit - Limit of Infinity

Limit - One-sided and Two-sided limits from the graph

Limit - One and Two sided limit from the Equation

Limit - Limit of Multi variables functions

Limit - Continuity & Discontinuity

Asymptote

Squeeze Theorem - Introduction and Proof

Squeeze Theorem - Problems with solutions

Logarithmic & Exponential Rules - Basic Rules

Logarithmic & Exponential Rules - Problems with solutions

Logarithmic & Exponential Functions - Extraneous Roots

Derivative/Differentiation - Basics and Pre-requisites

Derivative/Differentiation - Power Rule

Derivative/Differentiation - Difference Quotient Rule

Derivative/Differentiation - Quotient Rule

Derivative/Differentiation - Product Rule

Logarithmic & Exponential Differentiation - Derivative of Function to Function

Logarithmic & Exponential Differentiation - product and Fractional function

Chain Rule - Introduction to the Chain Rule

Chain Rule - Single Chain Rule

Chain Rule - Multi-Chain Rule

Chain Rule - Product Chain Rule

Chain Rule - Quotient Chain Rule

Trigonometric Functions - Graphical & Mathematical Proofs of trig functions

Trigonometric Functions - Substitute random values for trig with proofs

Trigonometric Functions - Solve trigonometric functions

Inverse Trigonometric functions

Hyperbolic Trigonometric functions - Basic & Proofs

Hyperbolic Trigonometric functions - Solve numerical

Inverse Hyperbolic Trigonometric Functions

Implicit Differentiation - Introduction to implicit differentiation

Implicit Differentiation - Method 1 to solve Implicit Differentiation

Implicit Differentiation - Method 2 to solve Implicit Differentiation

Implicit Differentiation - Line on the curve

Equation Modelling and solving the equation

Bonus Materials